What do you do when you feel homesick for a place that doesn't even exist..?

There's actually a word for that, called hiraeth. It's a bit hard to translate, as it is not from english, but some have defined it as 'remembering/longing something that you've never experienced'. :)

that depends on what you mean by "doesn't exist"
is this a place that you read about in a book or watched in a movie or series?? if it is, then i'd advise you to go roleplay the hell out of that place with characters you base on yourself. helps me anyway.

or.. is it a place that doesn't exist because it is an ideal you wish existed in the world but simply doesn't? if this is the case, that's a problem everyone struggles through and there's not usually a whole lot you can do about it.

if it's neither of those feel free to elaborate on your thought and I'll take it as a challenge to come up with something more useful to say than the nonsense already posted :)

Thank you both for those answers. I'll always keep them in mind. Hahaha, I love this site. Everyone does amazing things.